9. Решите уравнение 26 + 24 + 22 + ... + x = 126

Это арифметическая прогрессия с a₁ = 26, d = -2.

S_n = (2a₁ + (n-1)d) * n / 2 = 126

(2*26 + (n-1)*(-2)) * n / 2 = 126

(52 - 2n + 2) * n = 252 => (54 - 2n) * n = 252 => 2n² - 54n + 252 = 0 => n² - 27n + 126 = 0.

D = 27² - 4*126 = 729 - 504 = 225 => √D = 15.

n₁ = (27+15)/2 = 21, n₂ = (27-15)/2 = 6.

Если n=21, x = a₂₁ = 26 + (21-1)*(-2) = 26 - 40 = -14.

Если n=6, x = a₆ = 26 + (6-1)*(-2) = 26 - 10 = 16.